Publications from the Center of Mathematical Morphology

F. Willot, H. Trumel, D. Jeulin (2019): The thermoelastic response of cracked polycrystals with hexagonal symmetry. Philosophical Magazine 99(5) 606—630.The influence of a population of randomly-oriented cracks on the macroscopic thermal and linear-elastic response of a hexagonal polycrystal is addressed using a self-consistent method. Coupling between micro-cracks and crystal anisotropy is taken into account through the effective medium where all inhomogeneities are embedded. In the absence of cracks, the proposed approach reduces to the self-consistent estimate of Berryman (2005). The accuracy of the present method is first assessed using numerical, Fourier-based computations. In the absence of crystal anisotropy, the estimates for the...

A. Borocco, B. Marcotegui (2019): Non-rigid shape registration using curvature information. 14th International Conference on Computer Vision Theory and Applications, Prague (Czech Republic).This paper addresses a registration problem for an industrial control application: it meets the need to registrate a model on an image of a flexible object. We propose a non-rigid shape registration approach that deals with a great disparity of the number of points in the model and in the manufactured object. We have developed a method based on a classical minimization process combining a distance term and a regularization term. We observed that, even if the control points fall on the object boundary, the registration failed on high curvature points. In this paper we add a curvature-based...

R. Rodriguez Salas, P. Dokládal, E. Dokladalova (2019): Rotation-invariant NN for learning naturally un-oriented data. Deep convolutional neural networks accuracy is heavily impacted by the rotations of the input data. In this paper, we propose a convolutional predictor that is invariant to rotations in the input. This architecture is capable of predicting the angular orientation without angle-annotated data. Furthermore, the predictor maps continuously the random rotation of the input to a circular space of the prediction. For this purpose, we use the roto-translation properties existing in the Scattering Transform Networks with a series of 3D Convolutions. We validate the results by training with upright...

R. Rodriguez Salas, E. Dokladalova, P. Dokládal (2019): Rotation invariant CNN using scattering transform for image classification. Deep convolutional neural networks accuracy is heavily impacted by rotations of the input data. In this paper, we propose a convolutional predictor that is invariant to rotations in the input. This architecture is capable of predicting the angular orientation without angle-annotated data. Furthermore, the predictor maps continuously the random rotation of the input to a circular space of the prediction. For this purpose, we use the roto-translation properties existing in the Scattering Transform Networks with a series of 3D Convolutions. We validate the results by training with upright and...

P. Cettour-Janet, C. Cazorla, V. Machairas, Q. Delannoy, N. Bednarek, F. Rousseau, E. Decencière, N. Passat (2019): Watervoxels. In this article, we present the $n$-dimensional version of the waterpixels, namely the watervoxels. Waterpixels constitute a simple, yet efficient alternative to standard superpixel paradigms, initially developed in the field of computer vision for reducing the space cost of input images without altering the accuracy of further image processing / analysis procedures. Waterpixels were initially proposed in a 2-dimensional version. Their extension to 3-dimensions---and more generally $n$-dimensions---is however possible, in particular in the Cartesian grid. Indeed, waterpixels mainly rely on a...

E. Bazan, P. Dokládal, E. Dokladalova (2019): Quantitative Analysis of Similarity Measures of Distributions. The Earth Mover's Distance (EMD) is a metric based on the theory of optimal transport that has interesting geometrical properties for distributions comparison. However, the use of this measure is limited in comparison with other similarity measures as the Kullback-Leibler divergence. The main reason was, until recently, the computation complexity. In this paper, we present a comparative study of the dissimilarity measures most used in the literature for the comparison of distributions through a color-based image classification system and other simple examples with synthetic data. We show that...